Malgorzata Klimek

Solutions of Euler-Lagrange equations in fractional mechanics

A class of Euler-Lagrange equations in fractional mechanics is considered. They contain fractional differential operators of two types, namely Riemann-Liouville and Caputo derivatives. Applying Banach theorem on fixed points of contractive mappings we show that these equations have unique solutions. As an example the nonlinear fractional oscillator model is studied.